In ordinary English, the term “interaction” usually connotes some type of causal interaction among two or more factors in producing an effect ( Causation and Causal Inference). Formal versions of these ideas are discussed in the article Effect Modification and Biological Interaction. The present article concerns instead the common use of the term “interaction” in the statistics literature without explicit reference to causality.
In the context of regression modeling, the phrase “interaction term” or “interaction” is most often used as a synonym for a model term involving the product of two or more variables. Consider a logistic regression to predict a man’s actual sexual preference A (A = 1 for men, 0 for women) from his self-reported preference R in an interview, with G indicating the interviewer’s gender (G = 1 for male, 0 for female):
where expit(x) = e x ∕ (1 + e x) is the logistic...
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References and Further Reading
Greenland S, Poole C (1988) Invariants and noninvariants in the concept of interdependent effects. Scand J Work Env Hea 14:125–129
Greenland S, Lash TL, Rothman KJ (2008) Concepts of interaction, ch 5. In: Modern epidemiology, 3rd edn. Lippincott, Philadelphia, pp 71–83
Rothman KJ (1976) Causes. Am J Epidemiol 104:587–592
VanderWeele TJ, Robins JM (2007) The identification of synergism in the sufficient-component cause framework. Epidemiology 18:329–339
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Greenland, S. (2011). Interaction. In: Lovric, M. (eds) International Encyclopedia of Statistical Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04898-2_305
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DOI: https://doi.org/10.1007/978-3-642-04898-2_305
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